UNSUPERVISED LEARNING ON CITY OF SCOTTSDALE CITATIONS¶
Three clustering methods will be used to look for patterns in when different demographics receive certain types of citations. Specifically, clusters will be formed using CITATION TYPE, LOCATION, AGE, TIME OF DAY, DAY OF WEEK, and MONTH OF YEAR.¶
Applications for this Analysis:¶
By undersanding when and where certain demographics are more likely to receive citations the city could be more proactive in preventing the citations. Additionally, this could allow the city to be more effective in assigning its police force.
Selling services to people who receive citations:
- Lawyers or professionals providing services to people who receive and want to contest certain types of citations could use clustering information to inform where to market their services.
- Ride hailing services such as Lyft and Uber would benefit by being able to identify areas and specific times when people might be most likely to drive drunk. Using targeted advertising these companies can more effictively market their services and keep drunk drivers off the roads.
Providing information for citizens to be more careful within certain areas of the city. Similar to how the navigation app Waze crowd sources information to prevent people from receiving a ticket, identifying specific clusters and allerting people to them may prevent them from receiving citations.
Historical citations represent a picture of past policing practices. Understanding citation clusters in the past can provide a context for distributing policing forces in the future. Perhaps clusters are forming in some places simply because police officers perceive that policing that area to be the best use of their time. When in fact there are other areas that are being overlooked.
Table of Contents:¶
# finalized features
df.head()
EDA¶
# plot clusters in 3d
# degree controls horizontal view
# elev controls vertical view
def plot_3d(cluster1, cluster2=None, elev=None, degree=None):
fig = plt.figure(figsize=(12, 10))
ax = Axes3D(fig)
ax.scatter(df_clusters.loc[:,'cited_person_age'],
df_clusters.loc[:,'day_of_week'],
df_clusters.loc[:,'hour_of_day'],
c='grey',
alpha=.1,
label='All Citations')
ax.scatter(df_clusters[(df_clusters.cluster == cluster1) |
(df_clusters.cluster == cluster2)].loc[:,'cited_person_age'],
df_clusters[(df_clusters.cluster == cluster1) |
(df_clusters.cluster == cluster2)].loc[:,'day_of_week'],
df_clusters[(df_clusters.cluster == cluster1) |
(df_clusters.cluster == cluster2)].loc[:,'hour_of_day'],
c='red',
alpha=.8,
label='Cluster Citations')
if cluster2 != None:
ax.set_title('Clusters ' + str(cluster1) + ' & ' + str(cluster2), fontsize=25)
else:
ax.set_title('Cluster ' + str(cluster1), fontsize=25)
ax.legend(fontsize=16)
ax.set_xlabel('Age', fontsize=16)
ax.set_ylabel('Day of Week', fontsize=16)
ax.set_zlabel('Hour of Day', fontsize=16)
ax.view_init(degree, elev);
CLUSTER USING DBSCAN¶
This clustering method works by forming clusters based on the concentration and closeness of datapoints. I believe this clustering method will be helpful since:
- it doesn't require me to specify the number of clusters I expect to find in advace, and
- it can find clusters of any shape
# find best DBSCAN parameters
cluster_count = []
sil_score = []
eps_ = []
min_samples_ = []
for eps in [.1, .5, 1]:
for min_samples in [5, 10, 15]:
# Defining the agglomerative clustering
dbscan_cluster = DBSCAN(eps=eps, min_samples=min_samples)
# Fit model
clusters = dbscan_cluster.fit_predict(X_std)
# capture cluster count
cluster_count.append(len(set(clusters)) - (1 if -1 in clusters else 0))
# capture model fit
if pd.Series(clusters).nunique() > 1:
sil_score.append(round(metrics.silhouette_score(X_std, clusters, metric='euclidean'), 3))
else:
sil_score.append(np.nan)
# record parameter values
eps_.append(eps)
min_samples_.append(min_samples)
# tabulate param results from above
# sort by silhouette score & cluster count
cluster_scores = pd.DataFrame(list(list(zip(sil_score, cluster_count, eps_, min_samples_))),
columns=['sil_score', 'cluster_count', 'eps', 'min_samples']) \
.sort_values(by=['sil_score', 'cluster_count'], ascending=False)
cluster_scores
# plot silhouette score and cluster count
fig, (ax0, ax1) = plt.subplots(nrows=2,ncols=1, sharex=True, figsize=(10, 6))
cluster_scores.loc[:,['sil_score']] \
.plot(kind='bar', color='green', legend=False, ax=ax0)
ax0.set_title('SILHOUETTE SCORE', fontsize=15)
cluster_scores.loc[:,['cluster_count']] \
.plot(kind='bar', legend=False, ax=ax1);
ax1.set_title('CLUSTER COUNT', fontsize=15)
plt.xticks(rotation=1);
eps=1, min_sampels=5¶
dbscan_cluster = DBSCAN(eps=1, min_samples=5)
plt.figure(figsize=(6, 6))
clusters = dbscan_cluster.fit_predict(X_std)
pd.Series(clusters).value_counts().plot(kind='pie', title='Cluster Distribution')
plt.ylabel('');
With such a large number of clusters I focused on analyzing characteristics within the top 50.
pd.Series(clusters).value_counts()
# concat cluster numbers to dataset
df_clusters = pd.concat([df.reset_index(drop=True), pd.Series(clusters).rename('cluster')], axis=1)
# subset dataset based on top 50 clusters by size
df_clusters = df_clusters[df_clusters.cluster.isin(list(pd.Series(clusters).value_counts()[1:51].index))]
# how many citations are included in the
# top 50 clusters
df_clusters.shape
All the clusters are made up of one categorical variable each (citation type, and location).
- Both clusters 55 and 79 show similar characteristics - lower age and hour of the day with later day of the week.
- Cluster 101 and 98 represent the oldest people receiving citations, these are happening at a relatively early day of the day.
- Cluster 78 represents the youngest people receiving ciations.
- Cluster 58 represents the latest citations happening in the day, with no pattern in the age or time of day that these citations are issued.
Clusters 55 and 79¶
Both of these clusters represent 654 young people who receive DUI citations early in the day on the weekend within beats 5 & 6.
# how many people are included within these clusters
df_clusters[(df_clusters.cluster == 55) |
(df_clusters.cluster == 79)].shape
plot_3d(55, 79)
plot_3d(55, 79, 5, 80)
Cluster 58¶
This cluster represent the latest citations happening in the day. With little preference for age, this cluster is made up of 213 people received DUI citations exclusively within beat #6 very late in the evening.
plot_3d(58, None, 80, 5)
Clusters 101 and 98¶
These clusters represent 509 mostly older people who received citations at a relatively early hour of the day within beat locations 12 & 13.
plot_3d(98, 101, None, 5)
Cluster 78¶
This cluster represents the youngest mean age within a cluster with 360 people receiving citations for drug paraphernelia within beat 6. Most of these took place early in the day on the weekend.
plot_3d(78, None, 5,)
plot_3d(78, None, 5, 50)
fig, ax = plt.subplots(figsize=(10, 4))
cluster_attribute = 'day_of_week'
aggregator = 'charge_description'
df_cluster_sub = df_clusters[(df_clusters.cluster == 78)]
df_cluster_sub.groupby(['cluster', aggregator]).agg(['mean']).loc[:,[cluster_attribute]].reset_index().merge(
df.groupby([aggregator]).agg(['mean']).loc[:,[cluster_attribute]].reset_index(),
how='left',
on=aggregator,
suffixes=('_cluster', '_all_data')).set_index(['cluster', aggregator]).droplevel(level=1, axis=1).plot(ax=ax,
kind='bar',
alpha=.7)
plt.title('CLUSTER DIFFERENCES - ' + cluster_attribute.upper(), fontsize=14)
plt.ylabel(cluster_attribute)
plt.legend(loc='lower right')
plt.xticks(rotation=30, horizontalalignment="right");
eps=1, min_sampels=10¶
Examining the second best parameter configuration based on silhouette coefficient, I increased the min_samples parameter to 10.
plt.figure(figsize=(6, 6))
dbscan_cluster = DBSCAN(eps=1, min_samples=10)
clusters = dbscan_cluster.fit_predict(X_std)
pd.Series(clusters).value_counts().plot(kind='pie', title='Cluster Distribution');
Exploring parameters from the next highest silhouette coefficient, a larger share of citations are categorized as not fitting into any cluster.
Cluster #17 Summary:¶
This cluster is made up of 46 citations representing people who receive DUI tickets in beat #6. All of these tickets took place in the early morning hours on Sunday with an average month of the year of August. Additionaly, these tickets were received by people at least 10 year younger than average for this citation type.
Cluster #7 Summary:¶
This cluster is quite similar to cluster 17 above. It is made up of 79 citations representing people younger people who received DUI tickets in beat #6. The two exceptions from cluster 17 is that the average month of the year is August, and all these citations were received in the early morning on Saturday, rather than Sunday.
DBSCAN Clustering Summary:¶
This model did a good job of finding very tight clusters with highly similar characteristics. This model overwhelmingly clustered based off the categorical features (citation type, and location(beat)).
CLUSTER USING GMM¶
# find best GMM parameters
sil_score = []
num_components = []
cov_type = []
for n_components in range(10, 31, 5):
for covariance_type in ['full', 'tied', 'diag', 'spherical']:
# Defining the agglomerative clustering
gmm_cluster = GaussianMixture(n_components=n_components, covariance_type=covariance_type)
# Fit model
clusters = gmm_cluster.fit_predict(X_std)
sil_score.append(round(metrics.silhouette_score(X_std, clusters, metric='euclidean'), 3))
# record parameter values
num_components.append(n_components)
cov_type.append(covariance_type)
# tabulate param results from above
# sort by silhouette score & cluster count
cluster_scores = pd.DataFrame(list(list(zip(sil_score, num_components, cov_type))),
columns=['sil_score', 'num_components', 'covariance_type']) \
.sort_values(by=['sil_score'], ascending=False)
cluster_scores
# plot silhouette score and cluster count
fig, (ax0, ax1) = plt.subplots(nrows=2,ncols=1, sharex=True, figsize=(10, 6))
cluster_scores.loc[:,['sil_score']] \
.plot(kind='bar', color='green', legend=False, ax=ax0)
ax0.set_title('SILHOUETTE SCORE', fontsize=15)
cluster_scores.loc[:,['num_components']] \
.plot(kind='bar', legend=False, ax=ax1);
ax1.set_title('CLUSTER COUNT', fontsize=15)
plt.xticks(rotation=1);
The silhouette score at 25 components is significantly higher than that of DBSCAN at .197.
# create model
gmm_cluster = GaussianMixture(n_components=25, covariance_type='full', random_state=123)
plt.figure(figsize=(6, 6))
clusters = gmm_cluster.fit_predict(X_std)
pd.Series(clusters).value_counts().plot(kind='pie', title='Cluster Distribution')
plt.ylabel('');
Compared to DBSCAN, the size distribution of GMM is much more distributed.
# join cluster assignment to df
df_clusters = pd.concat([df.reset_index(drop=True), pd.Series(clusters).rename('cluster')], axis=1)
plot_clusters_scaled(df_clusters)
Unlike DBSCAN, GMM has multiple different citation types and locations within the clusters that it grouped.
EXAMINE SPECIFIC CLUSTERS THAT STAND OUT¶
Cluster 13¶
This cluster is made up of 980 citations for speeding in school zones. It has a high diversity of beat locations. This citation also happens mostly early in the morning, and almost exclusively early in the week.
df_clusters[df_clusters.cluster == 13].shape
plot_3d(13, None, 5, 60)
plot_clusters(df, df_clusters, 'beat', 'cited_person_age', 13)
plot_clusters(df, df_clusters, 'beat', 'hour_of_day', 13)
plot_clusters(df, df_clusters, 'beat', 'day_of_week', 13)
Cluster 24:¶
This cluster has the lowest mean age and is made up of 586 citations for drug parapharnelia that took place within three different beat locations. Most of these citations took place later in the week.
df_clusters[df_clusters.cluster == 24].shape
plot_3d(24, None, 5, 60)
plot_clusters(df, df_clusters, 'beat', 'day_of_week', 24)
plot_clusters(df, df_clusters, 'beat', 'cited_person_age', 24)
GMM Clustering Summary:¶
Although this model classified all citations into one of 25 clusters, the specific characteristics of each cluster were not as strong as those within the smaller DBSCAN clusters.
This model was able to cluster more strongly than DBSCAN using characteristics other than citation type and location. Whereas all the DBSCAN clusters were made up of onlye one citation type and one location, a number of GMM clusters included a number of unique citation types and locations.
HIERARCHICAL CLUSTERING¶
This method forms clusters based hierarchy structures within the data. Three different linkage methods exist - "ward", "complete", and "average". Since I'm not expecting clusters of equal sizes, and I'm intereested in tight clusters, I explored the "average" linkage method.
- Ward: The Ward method tends to look for spherical clusters such that the clusters are cohesive inside and differentiated from other groups. In general, this method tends to find clusters of similar size. Note that the Ward method only works with Euclidean distance.
- Complete: The Complete method links clusters using their furthest observations, that is, their most dissimilar data points. Consequently, clusters created using this method tend to be comprised of highly similar observations, making the resulting groups quite compact.
- Average: The Average method links clusters using their centroids. Since this method focuses on centroids and ignoring the boundary points, it tends to create larger groups than the complete method. Moreover, the clusters can be different sizes and shapes in contrast to the Ward method.
# plt.figure(figsize=(6, 6))
# agg_cluster = AgglomerativeClustering(linkage='average',
# affinity='cosine',
# n_clusters=13)
# clusters = agg_cluster.fit_predict(X_std)
# pd.Series(clusters).value_counts().plot(kind='pie', title='Cluster Distribution');
Running the above produced "MemoryError: unable to allocate array data." So I sampled 10000 citations below.
# select 10000 random rows
rand_index = np.random.choice(X_std.shape[0], size=10000)
# subset the full dataset
X_std_sample = X_std[rand_index,:]
# find best parameters
cluster_count = []
sil_score = []
cluster_param = []
for i in range(2, 50, 4):
# Defining the clustering model
agg_cluster = AgglomerativeClustering(linkage='complete',
affinity='cosine',
n_clusters=i)
# Fit model
clusters = agg_cluster.fit_predict(X_std_sample)
# capture cluster count
cluster_count.append(len(set(clusters)) - (1 if -1 in clusters else 0))
# capture model fit
if pd.Series(clusters).nunique() > 1:
sil_score.append(round(metrics.silhouette_score(X_std_sample, clusters, metric='euclidean'), 3))
else:
sil_score.append(np.nan)
# record parameter values
cluster_param.append(i)
# tabulate param results from above
# sort by silhouette score & cluster count
cluster_scores = pd.DataFrame(list(list(zip(sil_score, cluster_count, cluster_param))),
columns=['sil_score', 'cluster_count', 'cluster_param']) \
.sort_values(by=['sil_score', 'cluster_count'], ascending=False)
cluster_scores
# create clustering model
agg_cluster = AgglomerativeClustering(linkage='complete',
affinity='cosine',
n_clusters=50)
# use model to assign cluster labels
plt.figure(figsize=(6, 6))
clusters = agg_cluster.fit_predict(X_std_sample)
pd.Series(clusters).value_counts().plot(kind='pie', title='Cluster Distribution', )
plt.ylabel('');
# join cluster assignment to df
df_clusters = pd.concat([df.iloc[pd.Series(rand_index)].reset_index(drop=True),
pd.Series(clusters).rename('cluster')],
axis=1)
plot_clusters_scaled(df_clusters)
plot_3d(35, None, 5)
plot_3d(19, None, 5)
plot_3d(43, None, 5)
Hierarcical Clustering Summary:¶
Although the hierarchical model classified the citations into relatively small clusters with a silhouette coefficient slightly higher than DBSCAN, the specific characteristics of each cluster were not as strong as those within the DBSCAN clusters.
CONCLUSION/NEXT STEPS:¶
Clustering Method Comparison:¶
With an end goal of providing specific, actionable recommentations related to which areas of town have the highest concentrations of specific citations being received by people within different demographics DBSCAN was was the clear winner.
The clusters it revealed were not entirely surprising to me. If I were to focus on cluster groupings for clusters smaller than the top 50, its possible I find find others clusters that have more specific characteristics.
However, within the top 50 DBSCAN clusters, all the clusters were formed around a single citation and location. Clearly the categories were playing a disproportionate role in the clustering.
One admirable quality in GMM and Hierarcical clustering is their ability to include more than one citation type and location within each cluster. With enough tuning it may be possible I could get one of these models to identify clusters as tight as DBSCAN.
Next Steps:¶
- Examine clusters at a much smaller location level by concatenating street name with block number.
- Join additional datasets to the citation dataset. More features will likely allow for better clustering. Specifically, age demographics for specific areas of the city, or the most common business types in various ares of the city.
- Adjusting Hour_of_Day feature to account for rollover from midnight to early morning hours.